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Simplifying (a + -1b) * x2 + (b + -1c) * x + (c + -1a) = 0 Reorder the terms for easier multiplication: x2(a + -1b) + (b + -1c) * x + (c + -1a) = 0 (a * x2 + -1b * x2) + (b + -1c) * x + (c + -1a) = 0 (ax2 + -1bx2) + (b + -1c) * x + (c + -1a) = 0 Reorder the terms for easier multiplication: ax2 + -1bx2 + x(b + -1c) + (c + -1a) = 0 ax2 + -1bx2 + (b * x + -1c * x) + (c + -1a) = 0 ax2 + -1bx2 + (bx + -1cx) + (c + -1a) = 0 Reorder the terms: ax2 + -1bx2 + bx + -1cx + (-1a + c) = 0 Remove parenthesis around (-1a + c) ax2 + -1bx2 + bx + -1cx + -1a + c = 0 Reorder the terms: -1a + ax2 + bx + -1bx2 + c + -1cx = 0 Solving -1a + ax2 + bx + -1bx2 + c + -1cx = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1bx' to each side of the equation. -1a + ax2 + bx + -1bx2 + c + -1bx + -1cx = 0 + -1bx Reorder the terms: -1a + ax2 + bx + -1bx + -1bx2 + c + -1cx = 0 + -1bx Combine like terms: bx + -1bx = 0 -1a + ax2 + 0 + -1bx2 + c + -1cx = 0 + -1bx -1a + ax2 + -1bx2 + c + -1cx = 0 + -1bx Remove the zero: -1a + ax2 + -1bx2 + c + -1cx = -1bx Add 'bx2' to each side of the equation. -1a + ax2 + -1bx2 + c + bx2 + -1cx = -1bx + bx2 Reorder the terms: -1a + ax2 + -1bx2 + bx2 + c + -1cx = -1bx + bx2 Combine like terms: -1bx2 + bx2 = 0 -1a + ax2 + 0 + c + -1cx = -1bx + bx2 -1a + ax2 + c + -1cx = -1bx + bx2 Add '-1c' to each side of the equation. -1a + ax2 + c + -1c + -1cx = -1bx + bx2 + -1c Combine like terms: c + -1c = 0 -1a + ax2 + 0 + -1cx = -1bx + bx2 + -1c -1a + ax2 + -1cx = -1bx + bx2 + -1c Add 'cx' to each side of the equation. -1a + ax2 + -1cx + cx = -1bx + bx2 + -1c + cx Combine like terms: -1cx + cx = 0 -1a + ax2 + 0 = -1bx + bx2 + -1c + cx -1a + ax2 = -1bx + bx2 + -1c + cx Reorder the terms: -1a + ax2 + bx + -1bx2 + c + -1cx = -1bx + bx + bx2 + -1bx2 + -1c + c + cx + -1cx Combine like terms: -1bx + bx = 0 -1a + ax2 + bx + -1bx2 + c + -1cx = 0 + bx2 + -1bx2 + -1c + c + cx + -1cx -1a + ax2 + bx + -1bx2 + c + -1cx = bx2 + -1bx2 + -1c + c + cx + -1cx Combine like terms: bx2 + -1bx2 = 0 -1a + ax2 + bx + -1bx2 + c + -1cx = 0 + -1c + c + cx + -1cx -1a + ax2 + bx + -1bx2 + c + -1cx = -1c + c + cx + -1cx Combine like terms: -1c + c = 0 -1a + ax2 + bx + -1bx2 + c + -1cx = 0 + cx + -1cx -1a + ax2 + bx + -1bx2 + c + -1cx = cx + -1cx Combine like terms: cx + -1cx = 0 -1a + ax2 + bx + -1bx2 + c + -1cx = 0 The solution to this equation could not be determined.
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